Download - CCRMA - Stanford University

References
• Music -421 (EE 367B) Course Description
• J. 0 Smith. "Physical Modeling Synthesis Update". Computer Music Journal, vol. 20, no. 2.
pp. 44-56. Summer. 1996. Available online at http://wwv-ccnua.staiiiord.edu/~jos/.
• J. O. Smith. "Principles of Digital Waveguide Models of Musical Instruments.' in Applications of
Digital Signal Processing to Audio and Acoustics. Mark Kafirs and Karlheinz Brandenburg,
eds.. Kluwer Academic Publishers, pp. 417-466. 199S. See http: //www. wkap.nl/book .htm/0-7923-
-8130-0.
6.2.14 Signal Processing Algorithm Design Stressing Efficiency and Simplicity of Control
Timothy Stilson
This project deals with the design of digital filters, oscillators, and other structures that have parameters
that can be varied efficiently and intuitively. The main criteria for the algorithms are:
• Efficiency: The algorithms are intended to be as efficient as possible. This constraint is weighted
very high in design decisions.
• Non-Complexity of Controls: As a large part of efficiency, the amount of processing that must
be done on an input control to make it useful for the algorithm should be minimized. As an example,
some filter may have "center frequency" as a control input, but may actually go through a bunch
of expensive calculations to turn it into some lower level coefficients that are actually used in the
filter calculation. On the other hand, another filter may have design whereby center frequency goes
directly into the filter with little change, and the filter uses it in a rather simple calculation (i.e. the
ugly math hasn't simply been absorbed into the filter). This constraint often influences the choice
of basic algorithms, but also influences the control paradigms. For example, some algorithms may
turn out to be vastly more efficient if given some variation of frequency as an input, sav period,
or log(frequency). In order to remain efficient, the control paradigm may also need to change (the
whole system may use period rather than frequency, for example), otherwise there will need to be
excessive parameter conversions, which violate the control complexity criterion.
• Intuitiveness of Controls: As alluded to in the previous item, certain forms of controls can be
more efficient than others. Unfortunately, some efficient parameters may be hard to use for an
end-user. i.e. a musician will likely prefer to specify center frequency to a filter algorithm rather
than filter coefficients. In order to make algorithms usable, one must either introduce parameter
conversion procedures (inefficient) or look for an algorithm that has the desired inputs yet is more
efficient.
Often, one decides that a certain amount of inefficiency is livable, and in cases where a parameter
changes only rarely, large amounts of inefficiency can be tolerated. But when a parameter must change
very often, such as in a smooth sweep or a modulation, inefficiency is intolerable.
In this project, the main application is the field referred to as "Virtual Analog Synthesis', which tries to
implement analog synthesis algorithms (in particular, subtractive synthesis) in digital systems. Characteristics
of many analog patches were the blurring of the distinction between control signals and audio
signals, such as in modulation schemes, or the ability to dynamically (smoothly) control any parameter.
Both of these abilities require parameters to change at very high rates, even as fast as the sampling rate.
Thus the necessity for efficiently controllable algorithms.
Two subprojects within this project are currently under being researched. First: the design and implementation
of an efficient signal generator which generates bandlimited pulse trains, square waves.
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